Sören Sanders // Universität Oldenburg

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orcid.org/0000-0003-3933-4588

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S. Sanders und M. Holthaus, "Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model" New Journal of Physics, vol. 19, iss. 10, p. 103036.
@article{Sanders_2017a, author = {Sören Sanders and Martin Holthaus}, title = {{Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model}}, journal = {New Journal of Physics}, volume = {19}, number = {10}, pages = {103036}, url = {http://stacks.iop.org/1367-2630/19/i=10/a=103036}, year={2017}, abstract={We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.} }
[article] bibtex | Dokument aufrufen
S. Sanders und M. Holthaus, "Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation" Journal of Physics A: Mathematical and Theoretical, vol. 50, iss. 46, p. 465302.
@article{Sanders_2017b, author = {Sören Sanders and Martin Holthaus}, title = {{Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation}}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {50}, number = {46}, pages = {465302}, url = {http://stacks.iop.org/1751-8121/50/i=46/a=465302}, year = {2017}, abstract = {We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose–Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.}

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Sören Sanders

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